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Concept

Standard Form of a Quadratic Function

The standard form of a quadratic function is a quadratic function written in a specific format.

f(x)=ax2+bx+c

Here, a, b, and c are real numbers with a0. The term with the highest degree — the quadratic term — is written first. Then, the linear term followed by the constant term are written. The standard form can be used to determine the direction of the parabola, the y-intercept, the axis of symmetry, and the vertex.

Direction of the Graph Opens upward when a>0
Opens downward when a<0
y-intercept c
Axis of Symmetry
Vertex

Standard Form of a Quadratic Equation

Similar to a quadratic function, a quadratic equation can be written in standard form. This is called the standard form of a quadratic equation.
In this equation, a is not equal to 0. The solutions of a quadratic equation written in this form can be found by applying the Quadratic Formula.

Rewriting a Quadratic Function in Standard Form

Both the vertex and the intercept form of a quadratic function can always be written in standard form.

Form Equation How to Rewrite?
Vertex Form y=a(xh)2+k Expand (xh)2, distribute a, and combine like terms.
Intercept Form y=a(xp)(xq) Multiply a(xp)(xq) and combine like terms.

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